DECIDING BETWEEN I(0) AND I(1) VIA FLIL-BASED BOUNDS
利用函数迭代对数律构造边界，提出一种几乎必然一致的规则，用于判断时间序列是I(0)还是I(1)，并给出异方差情形下方差估计量强一致性的条件。
We construct properly scaled functions of R p -valued partial sums of demeaned data and derive bounds via the functional law of the iterated logarithm for strong mixing processes. If we obtain a value below or equal to the bound we decide in favor of I (0); otherwise we decide in favor of I (1). This provides a consistent rule for classifying time series as being I (1) or I (0). The nice feature of the procedure lies in the almost sure nature of the bound, guaranteeing a lim sup–type result. We finally provide conditions for the strong consistency of estimators of the variance in the dependent and heterogeneous case.